Dynamics of carrier populations and localized spins during magnetic-polaron formation in quantum dots*

We have extended our previous investigation of time evolution of PL from (Zn,Mn)Te/ZnSe quantum dots in a magnetic field $B$ [1]. PL studies at $T=$5 K in these type-II dots reveal formation of magnetic polarons (MP). We find their formation time $\tau_{MP}$ to be 0.5 ns, which varies little with $B$. The circular polarization $P$ of the emission shows a surprising behavior. For all fields, the characteristic time $\tau_{P}$ is longer than $\tau_{MP}$. Furthermore, $\tau_{P}$ decreases from 10 ns to 1.9 ns as $B$ increases from 1 to 4 tesla. We attribute this effect to a low-$B$ bottleneck in the $\sigma_{+}$ recombination channel, due to the almost equal populations of the spin $\pm 1/2$ electrons participating in the interband transitions. In contrast, the $\pm 3/2$ holes in the (Zn,Mn)Te QDs, are affected mostly by the effective field due to exchange interaction between hole and Mn spins around it. This effective field is much larger than $B$. \\[4pt] [1] I.R. Sellers \textit{et al}. Phys. Rev. B. 82, 195320 (2010)